As Victoria Donahue made her way to the batter’s box, her name rang out over the loudspeaker, and her image filled the big screen in centerfield. Adjusting a too-big helmet as she stepped to the plate Monday, the 12-year-old could not help but smile. She was up to bat at Fenway Park.

In a good-will gesture to fans who suffered through the worst Red Sox season in decades, the team opened up Fenway over the holiday weekend to season-ticket holders, giving diehard fans a chance to sit in the dugout, snap pictures in the clubhouse, and take aim at the Green Monster. Or at least the outfield grass.

It was the first time the team has held the three-day open house, and fans were well aware the timing was no coincidence. After the team’s unexpected last-place finish, a season marred by enough turmoil and dysfunction to fill a soap opera, frustration is running high, forcing the team into the unfamiliar position of having to appease its loyalest fans.

Fans said the chance to be on the field would not erase the disappointing season, or pay them back for all those games in August and September when the team was just playing out the string. But as public relations go, it was pretty nice.

“Were they doing this in 2007?” Joe Donahue, Victoria’s father, asked rhetorically, referring to the team’s last championship. “I don’t think so. But every bit of good will helps.”

After Victoria finished her turn, Donahue cheered on his daughter Isabelle, 11. Behind her, a long line of fans — mostly fathers in Red Sox garb with their kids in tow — waited their turn. Each batter got five pitches from a pitching machine.

“Good swing!” he shouted. “Almost.”

‘It was the first time in many years we knew there would be no games in October.’

Gerard Baer, 39, said the pitches came in faster than he expected, but he was able to make some solid contact. He had signed up for the batting practice as soon as he got word, and was soaking up every moment with his 3-year-old son.

“I’m loving it,” he said.

The team said that 2,000 season-ticket holders — out of about 22,000 — had signed up for the family-oriented event. With the team far from contention, the Red Sox began planning the open house in mid-September.

“It was a unique situation,” said Zineb Curran, a team spokeswoman. “It was the first time in many years we knew there would be no games in October.”

Curran said the offer was meant as a token of appreciation for the fans’ support during a “very disappointing” year. The team will send out season-ticket renewal forms next month. There is a waiting list of about 8,500 for season tickets, she said.

Although many batters swung for the fences, sometimes losing their balance in the process, no home runs were reported. About 30 to 40 people reached the wall though, an impressive feat.

The Red Sox have the highest ticket prices in baseball, but thanks to a intensely loyal fandom have sold out every game for years. This year, attendance fell off noticeably and tickets were easy to come by, and many criticized the sellout streak as a marketing ploy.

Charlie Domestico, a longtime season-ticket holder from Ashland, called the event a “terrific idea” and felt it was a genuine effort to thank the fans who show up in good years and bad.

“An exquisite touch to end a very difficult season,” said Domestico, 56, who was there with his son, daughter-in-law, and grandson.

Fans said the event would not affect their decision to renew their tickets either way, but they appreciated the gesture. Most predicted that the last-place finish was an aberration after a long run of success, and that the team would be good again before long. Even if that was wishful thinking, many have had their seats for years and can hardly imagine life without them.

Kids seemed to enjoy the event most of all. They marveled at the view from the field, and sat in the dugout like their favorite players. But their parents were close behind, often asking Fenway staff to snap pictures of the whole family.

Jen Perna, who came with her husband and three children, said the kids were over the moon to be on the field and in the dugout. And look, there was Wally, taking batting practice.

True fans, Perna said, love the team in down years, too, not just when they are winning.

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